Ms Thesis Presentation

TopicDYNAMIC HORIZONTAL AND VERTICAL

STIFFNESSES OF CAISSON FOUNDATIONS IN HOMOGENOUS SOIL

ADVISOR: Prof. Dr. Shahid AhmadCommittee Member: Prof. Dr. Sabanayagam Thevanayagam

Objective

To determine the horizontal and vertical stiffness and damping coefficients for caissons.

INTRODUCTION

Definition: Caissons, Pier or drilled shafts;• Massive Cylindrical Embedded Found, Precast or cast in place concrete with steel reinforcement and steel jacket or casing.• Diameter Range: 2-12 feet.• Depth to Dia ratio: 0.5-4Uses: 1. Bridge foundation elements2. Foundation components of transmission

towers3. Foundations at marine sites

Caisson

Schematic Diagram of circular Caisson.

D

B

LITERATURE REVIEW

• G. Gazetas (2005) Lateral Response of

Caissons of D/B=1-3 by Winkler model

• Varun et al. (2009) Lateral Response of

Caissons, D/B=1-6.

• Carolin Birk and Behnke (2010) dynamic

response of foundations by scaled boundary

finite element method.

• S. Ahmad, A.S.M. Israil and K. Chen (1988) Dynamic stiffness of rigid square and

rectangular foundations by DBEM and IBEM.

•S. Ahmad, A.K. Rupani (1999) Horizontal

impedance of square foundation in layered soil

• P. K. Pradhan et al (2004) presented vertical

dynamic response of foundation using Cone Model

• Iftekhar Anam and Jose M. Roesset (2004)

Dynamic stiffness’s of surface foundations

• Y. Q. Cai et al (2009) Vertical dynamic response of a

rigid foundation embedded in poroelastic soil layer.

• Artur Pais and Kausel (1988) Approximate

formulas for dynamic stiffness’s of rigid

foundations.

• H. L. Wong and J. E. Luco (1985) Tables of

impedance functions for square foundations on

layered media.

• S. Ahmad and A. Bharadwaj (1991) presented

horizontal impedance of embedded strip

foundations

CONVERGENCE STUDY OF BOUNDARY ELEMENT DISCRETIZATION AND COMPARISON WITH PUBLISHED

RESULTS

• Poisson’s ration= 0.35

• Shear Wave Velocity, Vs=1

• Radius of Caisson, B=1

• Normalized Elastic Modulus ES=2.7

.

Typical discretization pattern for embedded foundation over half-space

.

Surface Foundation Boundary Element Discretization (soil-foundation interface)

0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20

Vertical stiffness co-efficient

3 Elements2 Elements4 Elements

a0

kv

0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

Vertical Dashpot co-efficient

2 Elements3 Elements4 Elements

a0

Cv

.

Convergence study on free surface discretization for surface foundation

0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

Vertical Stiffness Co-efficient

3 B 7 B12 B Y. Q. Cai, Hong (2009)

a0

kv

0.00 0.50 1.00 1.50 2.00 2.500.00

0.50

1.00

1.50

2.00

2.50


3 B 7 B12 B Y. Q. Cai, Hong (2009)

a0

Cv

.

Convergence study on free surface discretization for caisson, D/B=6

0.00 0.20 0.40 0.60 0.80 1.00 1.200.00

0.20

0.40

0.60

0.80

1.00

1.20

Horizontal stiffness co-efficient

17 B 25 B Varun et al.(2009)

a0

kx

0.00 0.20 0.40 0.60 0.80 1.00 1.200.00

0.50

1.00

1.50

2.00

2.50

3.00

Horizontal dashpot co-efficient

17 B 25 B Varun et al.(2009)

a0

CX/E

S

RESULTS, COMPARISON AND DISCUSSIONS

Horizontal Static Stiffness of caissons.

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.00.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

Horizontal Static stiffness at different D/B

Present EPRI(1982)

D/B Ratio

kx(s

tatic

)

.

Vertical Static Stiffness of caissons

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.01.450

1.500

1.550

1.600

1.650

1.700

1.750

1.800

Vertical static Stiffness at different D/B

Kv Static

D/B Ratio

kv(S

tatic

)

.

Surface Foundation

0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

Vertical Stiffness co-efficient

Present Y.Q.Cai, Hong (2009)

a0

kv

0.00 0.50 1.00 1.50 2.00 2.500.00

0.50

1.00

1.50

2.00

2.50

Vertical Damping Coefficient

Present Y.Q.Cai, Hong(2009)

a0

Cv

.

Embedded Foundation of D/B=1, Vertical stiffness

0.00 0.50 1.00 1.50 2.00 2.50

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

Vertical Stiffness co-efficient

Present Birk & Behkne(2010)

a0

kv

0.00 0.50 1.00 1.50 2.00 2.500.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

Vertical Damping co-efficient

Present Birk & Biehkne(2010)

a0

Cv

.

Caissons vertical stiffness at different D/B ratio’s.

0.00 0.50 1.00 1.50 2.00 2.50

-35.00

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

5.00

Vertical Stiffness Co-efficient

D/B=2 D/B=3 D/B=4 D/B=6 D/B=8

a0

kv

0.00 0.50 1.00 1.50 2.00 2.500.00

1.00

2.00

3.00

4.00

5.00

6.00


D/B=2 D/B=3 D/B=4 D/B=6 D/B=8

a0

Cv

.

Embedded Foundation, D/B=2.

0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20


Present Varun et al.(2009)

a0

kx

0.00 0.50 1.00 1.50 2.00 2.500.000.200.400.600.801.001.201.401.601.802.00

Horizontal dashpot co-efficient


a0

Cx/E

s

.

Caissons of D/B=4, Horizontal Stiffness.

0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20



a0

kx

0.00 0.50 1.00 1.50 2.00 2.500.00

0.50

1.00

1.50

2.00

2.50

3.00

Horizontal Damping co-efficient


a0

Cx/E

s

.


0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20


Present Varun et al.(2009).

a0

kx

0.00 0.50 1.00 1.50 2.00 2.500.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50


Present Varun et al.(2009.

a0

Cx/E

s

.


0.00 0.50 1.00 1.50 2.00 2.500.00

0.20

0.40

0.60

0.80

1.00

1.20


Present

a0

kx

0.00 0.50 1.00 1.50 2.00 2.500.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00


Present

a0

Cx/E

s

ConclusionResults for vertical and horizontal stiffness and damping coefficients are available in layered and non-homogeneous media. The results were taken over homogeneous half-space and compared with available results.

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